Question

Write a power function representing the verbal statement. (Let k represent the constant of proportionality)

Answer 1

The Power function representing the verbal statement is W = k.$n^{1/2}$.

What is the Power function?

A power function is in the form of f(x) = kxⁿ, where k = all real numbers and n = all real numbers. You can change the way the graph of a power function looks by changing the values of k and n.

When two quantities are proportional, their relationship can be described by the linear equation y = kx, where k is the constant of proportionality.

Now "inversely proportional to the square root" is the same as "proportional to the inverse of the square root."

According to question,

       W α 1/√n

      W = k/√n

      W = k.$n^{-1/2}$

Thus, the Power function representing the verbal statement is W = k

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Answer 2

Answer:

  W = k·n^(-1/2)

Step-by-step explanation:

When two quantities are proportional, their relationship can be described by the linear equation y = kx, where k is the constant of proportionality.

Saying two quantities are inversely proportional is the same as saying one is proportional to the inverse of the other. Then "inversely proportional to the square root" is the same as "proportional to the inverse of the square root."

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W is inversely proportional to the square root of n, so we have ...

  $W=k\cdot\dfrac{1}{\sqrt{n}} = \dfrac{k}{n^{\frac{1}{2}}}\\\\\boxed{W=kn^{-\frac{1}{2}}}$

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Additional comment

The rules of exponents let us write the square root as a fractional power, and the inverse as a negative power. Thus our power function ends up with a negative fractional power.